If a surface is hot enough it can vapourise the bottom of a droplet and , because water vapour is a poor conductor, the unvapourised water sits on a 'cloud' of steam. This is what makes a drop of water 'dance around' on a frying pan or hotplate. This is called the Leidenfrost effect. The same effect can be used to plunge a wet hand into molten lead uninjured and has been suggested as an explanation of fire walking. The people who walk over hot coals in bare feet often walk on wet grass first.

My understanding of how the 'uphill water' works is that there are repeated small slopes on the surface which act to direct the pressure of this steam layer so as to force the droplet in a particular direction. This means that one can control the way the droplet moves by the design of the pattern of slopes. So instead of dancing around randomly it goes where you want it to go. The 'uphill' bit is slightly misleading, though it does seem possible to drive it up a small gradient this way. Very clever!

Capillary action is a different thing and relies on surface tension I think.